In this paper we analyze a simple model of adaptive competition which captures essential features of a variety of adaptive competitive systems in the social and biological sciences. In this model, each of N agents, at each time step of a game, joins one of two groups. The agents in the minority group are awarded a point, while the agents in the majority group get nothing. Each agent has a fixed...

In noncommutative spaces, it is unknown whether the Pontrjagin class gives integer, as well as, the relation between the instanton number and Pontrjagin class is not clear. Where we define “Instanton number” by the size of Bα in the ADHM construction. We show the analytical derivation of the noncommuatative U(1) instanton number as an integral of Pontrjagin class (instanton charge) with the Foc...

In this article, the core results of the author’s papers are summarized. The author’s work has been carried out mainly on the finite field analogues of classical problems in harmonic analysis, geometric measure theory, and combinatorics. In particular, the author has investigated the boundedness of extension operators and the Erdős-Falconer type distance problems in the finite field setting. Th...

Lattice tests are quality measures for assessing the intrinsic structure of pseudorandom number generators. Recently a new lattice test has been introduced by Niederreiter and Winterhof. In this paper, we present a general inequality that is satisfied by any periodic sequence. Then, we analyze the behavior of the linear congruential generators on elliptic curves (abbr. EC-LCG) under this new la...

During experiments employing Perruchet's (1985) paradigm there are runs of reinforced (CS-US) trials and non-reinforced (CS-noUS) trials. Conditioned responding (CR) is measured, for example, using eyeblink responses (Perruchet, 1985), reaction times (Perruchet, Cleeremans, & Destrebeceqz, 2006), or changes in skin conductance (SCR; McAndrew, Jones, McLaren, & McLaren, 2012), as well as an onli...

The present thesis deals with computable functional analysis and in this context, especially, with compact operators on computable Banach spaces. For this purpose, the representation based approach to computable analysis (TTE) is used. In the first part, computable Banach spaces with computable Schauder bases are introduced and two representations each are defined for the dual space of a comput...

Every Grassmannian, in its Plücker embedding, is defined by quadratic polynomials. We prove a vast, qualitative, generalisation of this fact to Plücker varieties, which are families of varieties in exterior powers of vector spaces that, like Grassmannians, are functorial in the vector space and behave well under duals. A special case of our result says that for each fixed natural number k, the ...

We look for geometric structures which underlie both the 'classical' geometric and more modern 'order theoretic' conditions for a Banach space (dual space) to have the weak (weak*) fixed point property; that is, for every nonexpansive self-mapping of a nonempty weak (weak*) compact convex subset to have a fixed point.

a heyting algebra is a distributive lattice with implication and a dual $bck$-algebra is an algebraic system having as models logical systems equipped with implication. the aim of this paper is to investigate the relation of heyting algebras between dual $bck$-algebras. we define notions of $i$-invariant and $m$-invariant on dual $bck$-semilattices and prove that a heyting semilattice is equiva...

The dual-route models of action imitation predict that, normally, known actions are imitated by using a semantic route i.e. by activating a representation of the action from memory whereas unknown, new actions are reproduced by using a direct route i.e. by performing a visuo-motor transformation of the input into an output. Here we aimed at establishing the nature of the dominant process used b...